In this paper we propose a novel high-dimensional estimation framework for penalized parametric frailty-based illness-death models. A critical challenge in this setting, however, is that the likelihood-based loss function is non-convex. This, in turn, renders the development of theoretical results and efficient computational tools particularly difficult. Moreover, to the best of our knowledge no prior literature has shown theoretical statistical properties of penalized frailty-based illness-death models.
In relevant work, [1]} prove error bounds for non-convex loss functions with non-convex penalties, but only verify conditions for select classes of linear and generalized linear models. Taking into account these various issues, the contributions of this paper are threefold. First, we propose a framework for selecting sparse covariate sets for each submodel via individual non-convex penalties, while inducing parsimony via a fused penalty on effects shared across submodels. Secondly, we develop an efficient optimization algorithm coupling a proximal gradient method with a pathwise routine to tune the model over a grid of regularization parameters. Finally, we prove high-dimensional statistical error bounds for a penalized frailty-based illness-death model estimator, expanding the literature on high-dimensional inference with non-convex losses and non-convex penalties. We present a simulation study investigating estimation and model selection properties, and develop a joint risk model for PE and delivery using real pregnancy outcome data from electronic health records.
